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Not sure whether they adjust for the forward curve or not.
Only insofar as the variable rate includes a risk premium above the risk free rate, of which volatility in the interest rate curve is a factor.
It's the fixed rate that is most dependent on forward rates.
It doesn't really make sense to measure lifetime payments based on anything other the current variable rate - otherwise you're looking at a level of sophistication beyond most people's needs, with reval curves, discount curves and the like.
Except the variable rate is...variable. So how do they calculate the cost? Some kind of average case scenario?